2023/05/23 by Benedict Bauer, Stefan Gerhold, Bauer, Benedict +1
Mathematics · Physics and Astronomy · #15A16 #26D15 #33C10 #33C45 #Advanced Thermodynamics and Statistical Mechanics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications
paper · pdf · doi:10.48550/arxiv.2305.14015
openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We argue that a classical inequality due to Fan, Taussky and Todd (1955) is equivalent to the dissipativity of a Jordan block. As the latter can be characterised via the zeros of Chebyshev polynomials, we obtain a short new proof of the inequality. Three other inequalities of Fan-Taussky-Todd are reproven similarly. By the Lumer-Phillips theorem, the semigroup defined by the Jordan block is contractive. This yields new extensions of the classical Fan-Taussky-Todd inequalities. As an application, we give an estimate for the partial sums of a Bessel function.